ITVOLT: An Iterative Solver for the Time-Dependent Schrödinger Equation

Abstract

We present a novel approach for solving the time-dependent Schrödinger equation (TDSE). The method we propose converts the TDSE to an equivalent Volterra integral equation; introducing a global Lagrange interpolation of the integrand transforms the equation to a linear system, which is then solved iteratively. In this paper, we derive the method, explore its performance on several examples, and discuss the corresponding numerical details.

arXiv commentThe updated version focuses exclusively on the time-dependent Schrödinger equation and includes both a new variant of the method and a more rigorous performance analysis. Contents: 20 pages, 5 figures, 2 tables

References in corpus (4)

• The Magnus expansion and some of its applications
• Semi-global approach for propagation of the time-dependent Schrödinger equation for time-dependent and nonlinear problems
• A Chebychev propagator with iterative time ordering for explicitly time-dependent Hamiltonians
• Multielectron effect in the strong-field ionization of aligned nonpolar molecules